A world where all actions are primarily motivated by self interest is a world where everyone in your life is only your friend/spouse/parent because they get something out of it. Your intrinsic value is secondary to their self-interest.
It's a world of takers, and the only 'true' answer to any request is 'what's in it for me?'
I have to emphasise that these decisions are being made on an unconscious level (or in the "Id", if you prefer the Freudian version). People (in general) aren't standing around consciously thinking to themselves "What's in it for me?", their unconscious is making the decisions it thinks is best for itself and then we consciously rationalise those decisions afterwards, usually without even realising that that's what we're doing (a recent study showed that - even with simple yes/no choices - the subconscious mind makes a decision anywhere up to
6 seconds before we consciously "decide" what choice we're going to make).
Even on a biological level it's what we're programmed to do (if you agree with Richard Dawkins about the selfish gene theory), we make decisions based on ensuring the survival of our particular genetic code, which is part of the reason why parents (usually) put their children's well-being ahead of their own.
As for friends seeing you in terms of what you can do for them, that's
exactly what we all do. We determine who our friends are based on what we bring to each other, and I say "each other" because if helping a friend or simply even making them feel good makes
you feel good, then it helps to create a reciprocal cycle of giving between you.
If someone doesn't make me feel good when I'm around them, why would I call them a friend? Wouldn't it make more sense to be friends with people who make you feel good? (It's important to note that I'm talking over the long term. Everyone has bad days and it isn't in our best interest to make snap decisions about people based on limited interaction with them).
There's a pretty simple answer to the concern that a world motivated by self-interest would be a cold and uncaring place where people simply use others and ignore their "intrinsic value", and that is to consciously invent reasons to care, because as CBT shows concious thought patterns can eventually become ingrained on an unconscious level.
For example, like Billy we could decide that helping others is the "right thing" to do, we would then be motivated to offer help to others because to do otherwise would make us feel bad. Alternatively we could develop a holistic empathy towards others, which would have the same effect, with the addition that it would begin to create a balancing point between using others and respecting their "intrinsic value".